Analytical method for evaluating the effective molecular diffusion coefficient within porous media

This paper presents an original analytical method for calculating the value of the effective molecular diffusion coefficient of an inert tracer transported within a saturated porous medium, D_m, in terms of the bulk diffusion constant, D_o. A simple three-step sequence in the tracer core or packed-bed flood is proposed involving (i) a (convection-dominated) tracer slug injection, (ii) a shut in to allow the slug to spread by diffusion and, finally, (iii) a postflush of the tracer slug by tracer-free solvent. The effluent profile from this sequence can be compared with a profile where no diffusive step [stage (ii)] was present. The difference in the effluents-the diffusive case will be more spread out in time-is purely due to the effects of molecular diffusion within the porous medium. The flood sequence is described by the convection-dispersion equation in stages (i) and (iii) and by the diffusion equation for stage (ii). Green's function propagator and analytical solutions for each step in the above process are well known for certain boundary conditions. We apply Green's function method to propagate the solution through each stage of the process using the final solution to the previous stage as the initial conditions for the next. The final expression for the effluent profile is complex but can easily be evaluated in closed form, and we have confirmed this by comparison with numerical results. The method is applied to sample experimental tracer effluent results in order to evaluate D_m of chloride within a sand pack. This comparison showed that a reasonable match to the effluent was found for D_m˜0.75D_o. © 1993.